Question

The graphs of the equations 2x+5y=3 and 2x+5y=7 are parallel lines. Find the equation of the line that is parallel to both lines and lies midway between them.

Answer 1

Re-write both equations into the slope-intercept form. 

y = mx + b 

1) 2x + 5y = 3

5y = -2x + 3

Divide all terms by 5. 

y = $-\frac{2}{5}x$ + $\frac{3}{5}$

2) 2x+5y=7

5y = -2x + 7 

y = $- \frac{2}{5}x$ + $\frac{7}{5}$

Now that both equations are in standard form, we know that the equation of the line that is parallel to both lines must have the same slope as the two lines which is -2/5. 

In order to find the y-intercept of the line, we have to add up the y-intercepts of the two lines and divide them by 2. 

$\frac{3}{5}$ + $\frac{7}{5}$

= $\frac{10}{5}$ ÷ 2 

= 2 ÷ 2

= 1

The y-intercept of the equation is 1. 

The equation of the line that is parallel to both lines and lies midway between them will have the slope of $-\frac{2}{5}x$ and a y-intercept of 1. 

Solution: y = $-\frac{2}{5}x$ + 1

Answer 2

The work to answer the problem is attached as a picture.